0606/21 May/Jun 2025, Question 6: The Binomial Expansion
Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 6 marks
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The question, in short
Expand a quadratic expression raised to power 5 up to three terms in ascending powers of x, and find the constant term in a separate binomial expansion.
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Part (a) · 4 marks
Factorise the quadratic 9x² + 12x + 4, then use the binomial expansion to give the first three terms in ascending powers of x, simplifying coefficients.
- 19x² + 12x + 4 = (3x + 2)²
- 2So (9x² + 12x + 4)⁵ = (3x + 2)¹⁰ = (2 + 3x)¹⁰
- 3= 2¹⁰ + 10(2⁹)(3x) + 45(2⁸)(3x)² + …
- 4= 1024 + 15 360x + 103 680x² + …
Answer1024 + 15 360x + 103 680x²
Part (b) · 2 marks
In the expansion of (6/x² + x⁴/2)¹², find the term that does not contain x.
- 1General term: ¹²Cᵣ (6/x²)^(12 − r) (x⁴/2)^r
- 2Power of x: −2(12 − r) + 4r = 0, so r = 4
- 3Term = ¹²C₄ × 6⁸ × (1/2)⁴ = 495 × 1 679 616 / 16
- 4= 51 963 120
Answer51 963 120
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Also searched as: 0606/21/M/J/25 · 0606_s25_qp_21 · 0606 s25 21 · question 6.
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